Events
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Algebra and Combinatorics Seminar: Corey Jones, NC State, Quantum cellular automata on fusion spin chains
Algebra and Combinatorics Seminar: Corey Jones, NC State, Quantum cellular automata on fusion spin chains
Quantum cellular automata (QCA) are models of discrete-time unitary dynamics of quantum spin systems. They can be characterized algebraically as certain automorphisms of the associative algebra generated by local observables of a spin system. We will give a gentle introduction to this topic, and explain some of our recent contributions to the problem of classification…
Nonlinear Analysis Seminar and Differential Equation Seminar: Shaoming Guo, University of Wisconsin Madison, Oscillatory integral operators on manifolds and related Kakeya and Nikodym problems
Nonlinear Analysis Seminar and Differential Equation Seminar: Shaoming Guo, University of Wisconsin Madison, Oscillatory integral operators on manifolds and related Kakeya and Nikodym problems
The talk is about oscillatory integral operators on manifolds. Manifolds of constant sectional curvatures are particularly interesting, and we will see that very good estimates on these manifolds can be expected. We will also discuss Kakeya and Nikodym problems on general manifolds, in particular, manifolds satisfying Sogge’s chaotic curvatures.
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Teaching and Learning Seminar: Matthew Voigt, Clemson University, Engaging in Critical Transformation of Math Programs to Disrupt the System
Teaching and Learning Seminar: Matthew Voigt, Clemson University, Engaging in Critical Transformation of Math Programs to Disrupt the System
In this interactive seminar, we will examine how data (qualitative and quantitative) can be leveraged to interrogate, disrupt, and enact changes in introductory math programs. In particular, I will share insights from the ACT UP Math project, which is studying the role and impact of research-practice partnerships between mathematics education experts and mathematics department faculty…
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Geometry and Topology Seminar: Marithania Silvero Casanova, Universidad de Sevilla, Positivity, fiberedness and link homology
Geometry and Topology Seminar: Marithania Silvero Casanova, Universidad de Sevilla, Positivity, fiberedness and link homology
Khovanov homology is a link invariant which categorifies Jones polynomial. In this talk we present several results concerning Khovanov homology of fibered positive links; in particular, we extend the result by Stosic stating that braid positive links have vanishing Khovanov homology in homological grading 1. We also explore Khovanov homology of certain cable links and…
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Applied Math Graduate Student Seminar:John Darges, NC State, Goal-Oriented Variance-Based Sensitivity Analysis for Uncovering Prior Hyperparameter Importance in Bayesian Inverse Problems s
Applied Math Graduate Student Seminar:John Darges, NC State, Goal-Oriented Variance-Based Sensitivity Analysis for Uncovering Prior Hyperparameter Importance in Bayesian Inverse Problems s
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of the hyperparameters defining the prior on the posterior statistics of the quantities of interest. Our approach relies on global sensitivity analysis (GSA) of…
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Algebra and Combinatorics Seminar: Mark Skandera, Lehigh University, Type-BC analogs of codominant permutations and unit interval orders
Algebra and Combinatorics Seminar: Mark Skandera, Lehigh University, Type-BC analogs of codominant permutations and unit interval orders
Permutations $w$ in $S_n$ for which the (type-A) Schubert variety $\Omega_w$ is smooth are characterized by avoidance of the patterns 3412 and 4231. The smaller family of codominant permutations, those avoiding the pattern 312, seems to explain a lot about character evaluations at Kazhdan-Lusztig basis elements $C'_w(q)$ of the (type-A) Hecke algebra. In particular, for…
Nonlinear Analysis Seminar and Differential Equation Seminar: Weinan Wang, University of Oklahoma, Global well-posedness and the stabilization phenomenon for some two-dimensional fluid equations
Nonlinear Analysis Seminar and Differential Equation Seminar: Weinan Wang, University of Oklahoma, Global well-posedness and the stabilization phenomenon for some two-dimensional fluid equations
In this talk, I will talk about some recent well-posedness and stability results for several fluid models in 2D. More precisely, I will discuss the global well-posedness for the 2D Boussinesq equations with fractional dissipation. For the Oldroyd-B model, we show that small smooth data lead to global and stable solutions. When Navier-Stokes is coupled…
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Geometry and Topology Seminar: Daniel Weser, UNC, A Heintze-Karcher inequality with free boundaries and applications to capillarity theory
Geometry and Topology Seminar: Daniel Weser, UNC, A Heintze-Karcher inequality with free boundaries and applications to capillarity theory
In volume-constrained capillarity problems, minimizers may have free boundaries adhering to the container. Recent work in the study of capillarity problems has utilized stability theory for the volume-constrained isoperimetric problem to classify the shape of global minimizers and (in the case without free boundary) critical points. In this talk, I will discuss joint work with…
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Nonlinear Analysis Seminar and Differential Equation Seminar: Eduardo Casas Renteria, University of Cantabria, Second Order Analysis for Optimal Control Problems
Nonlinear Analysis Seminar and Differential Equation Seminar: Eduardo Casas Renteria, University of Cantabria, Second Order Analysis for Optimal Control Problems
In this talk, we discuss second-order optimality conditions for optimal control problems. This analysis is very important when we study the stability of the solution to the control problem with respect to small perturbations of the data. It is also crucial for proving superlinear or quadratic convergence of numerical algorithms for solving the problem, as…
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Computational and Applied Mathematics Seminar: Dimitris Giannakis, Dartmouth, Quantum Information Science for Modeling Classical Dynamics
Computational and Applied Mathematics Seminar: Dimitris Giannakis, Dartmouth, Quantum Information Science for Modeling Classical Dynamics
Over the past three decades, a fruitful approach for analysis and data-driven modeling of dynamical systems has been to consider the action of (nonlinear) dynamics in state space on linear spaces of observables. These methods leverage the linearity of the associated evolution operators, namely the Koopman and transfer operators, to carry out tasks such as…
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Biomathematics Seminar: Benjamin Randall, NC State Alum, Physiology-informed machine learning: a biologically constrained, data-driven approach to cardiovascular health
Biomathematics Seminar: Benjamin Randall, NC State Alum, Physiology-informed machine learning: a biologically constrained, data-driven approach to cardiovascular health
Zoom Meeting: https://ncsu.zoom.us/j/93046132033?pwd=dkZiTjlKazgzK2Q3aXJra1g2R1Q0dz09 Meeting ID: 930 4613 2033 Passcode: 075251
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Nonlinear Analysis Seminar and Differential Equation Seminar:Giuseppe Buttazzo, University of Pisa, Italy, Antagonistic cost functionals in shape optimization
Nonlinear Analysis Seminar and Differential Equation Seminar:Giuseppe Buttazzo, University of Pisa, Italy, Antagonistic cost functionals in shape optimization
In several shape optimization problems one has to deal with cost functionals of the form ${\cal F}(\Omega)=F(\Omega)+kG(\Omega)$, where $F$ and $G$ are two shape functionals with a different monotonicity behavior and $\Omega$ varies in the class of domains with prescribed measure. In particular, the cost functional ${\cal F}(\Omega)$ is not monotone with respect to $\Omega$…
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Computational and Applied Mathematics Seminar:Tibor Illés, Corvinus University, Budapest, Hungary, Sufficient linear complementarity problems: pivot versus interior point algorithms
Computational and Applied Mathematics Seminar:Tibor Illés, Corvinus University, Budapest, Hungary, Sufficient linear complementarity problems: pivot versus interior point algorithms
Linear complementarity problems (LCP) generalizes some fundamental problems of mathematical optimization like linear programming (LP) problem, linearly constrained quadratic programming (LQP) problem and some others. It admits an enormous number of applications in economics, engineering, science, and many other fields. After all these, it is not surprising that LCPs are usually NP-complete problems (S.J. Chung,…
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Applied Math Graduate Student Seminar: Abhijit Chowdhary, NC State, Scalable Sensitivity Analysis and Optimal Design for Bayesian Inverse Problems
Applied Math Graduate Student Seminar: Abhijit Chowdhary, NC State, Scalable Sensitivity Analysis and Optimal Design for Bayesian Inverse Problems
Inverse problems are an expanding field with many practical applications in scientific computing and engineering. Their Bayesian enhancement encodes prior knowledge and data uncertainties into a posterior. This is an important tool in uncertainty quantification. However, performing uncertainty quantification tasks on top of this posterior is difficult to formulate and often computationally intractable. Hence, for…
Colloquium: Moody Chu, NC State, Optimal Hamiltonian Synthesis for Quantum Computing
Colloquium: Moody Chu, NC State, Optimal Hamiltonian Synthesis for Quantum Computing
Simulating the time evolution of a Hamiltonian system on a classical computer is hard—the computational power required to even describe a quantum system scales exponentially with the number of its constituents, let alone integrating its equations of motion. Hamiltonian simulation on a quantum machine is a possible solution to this challenge. Assuming that a quantum…
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Biomathematics Seminar: Yutong Sha, University of California Irvine, Reconstructing transition dynamics from static single-cell genomic data
Biomathematics Seminar: Yutong Sha, University of California Irvine, Reconstructing transition dynamics from static single-cell genomic data
Recently, single-cell transcriptomics has provided a powerful approach to investigate cellular properties in unprecedented resolution. However, given a small number of temporal snapshots of single-cell transcriptomics, how to connect them to obtain their collective dynamical information remains an unexplored area. One major challenge to connecting temporal snapshots is that cells measured at one temporal point…
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Algebra and Combinatorics Seminar: Joel Brewster Lewis, George Washington University, Bargain hunting in a Coxeter group
Algebra and Combinatorics Seminar: Joel Brewster Lewis, George Washington University, Bargain hunting in a Coxeter group
Petersen and Tenner defined the depth statistic for Coxeter group elements which, in the symmetric group, can be described in terms of a cost-minimization problem over the factorizations of a permutation into transpositions. We generalize that cost function to the other classical (finite and affine) Weyl groups, letting the cost of an individual reflection t…
Nonlinear Analysis Seminar and Differential Equation Seminar: Alex Dunlap, Duke University, Stochastic heat equations and Cauchy distributions
Nonlinear Analysis Seminar and Differential Equation Seminar: Alex Dunlap, Duke University, Stochastic heat equations and Cauchy distributions
I will describe how an invariant measure with Cauchy-distributed marginals arises from a supercritical stochastic heat equation with an additional, independent additive noise. Joint work with Chiranjib Mukherjee. Zoom meeting: Link
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Teaching and Learning Seminar: Kylan Schatz, Luke Castle, Tiancheng Xue, Lightning Talks
Teaching and Learning Seminar: Kylan Schatz, Luke Castle, Tiancheng Xue, Lightning Talks
Once per semester, the Teaching and Learning Seminar will host 10-minute "lightning talks" in which graduate students and/or faculty members will talk about some element of their teaching that they'd like to share. This may be a cool example you came up with for a class you are teaching, an innovative teaching technique or application…
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Computational and Applied Mathematics Seminar: Ke Chen, Maryland, Towards efficient deep operator learning for forward and inverse PDEs: theory and algorithms
Computational and Applied Mathematics Seminar: Ke Chen, Maryland, Towards efficient deep operator learning for forward and inverse PDEs: theory and algorithms
Deep neural networks (DNNs) have been a successful model across diverse machine learning tasks, increasingly capturing the interest for their potential in engineering problems where PDEs have long been the dominant model. This talk delves into efficient training for PDE operator learning in both the forward and the inverse problems setting. Firstly, we address the curse…
Geometry and Topology Seminar: Kai-Wei Zhao, University of Notre Dame, On the blowup of regularized solutions to the Jang equation and constant expansion surfaces
Geometry and Topology Seminar: Kai-Wei Zhao, University of Notre Dame, On the blowup of regularized solutions to the Jang equation and constant expansion surfaces
Schoen-Yau proved the spacetime positive energy theorem by reducing it to the time-symmetric (Riemannian) case using the Jang equation. To acquire solutions to the Jang equation, they introduced a family of regularized equations and took the limit of regularized solutions, whereas a sequence of regularized solutions could blow up in some bounded regions enclosed by apparent horizons. They analyzed the blowup behavior near and outside the apparent horizons, but what happens inside…
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Applied Math Graduate Student Seminar: Harley Hanes, NC State, Boundary Quantification and Optimal Sample Identification in Reduced-Order Models
Applied Math Graduate Student Seminar: Harley Hanes, NC State, Boundary Quantification and Optimal Sample Identification in Reduced-Order Models
Reduced-order models (ROMs) are a critical tool for sensitivity analysis, parameter inference, and uncertainty quantification where high-fidelity models would be computationally intractable. Galerkin POD-ROMs are one particular class of ROMs which project high-fidelity model equations onto a set of model solutions to construct ROMs retaining original model parameters and physics, enabling accurate sensitivity analysis, parameter inference,…
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Biomathematics Seminar: Carrie Manore, An Integrated Approach to Modeling Climate-Driven Pathogen Spread
Biomathematics Seminar: Carrie Manore, An Integrated Approach to Modeling Climate-Driven Pathogen Spread
Zoom Meeting: https://ncsu.zoom.us/j/93046132033?pwd=dkZiTjlKazgzK2Q3aXJra1g2R1Q0dz09 Meeting ID: 930 4613 2033 Passcode: 075251
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Algebra and Combinatorics Seminar: Kyle Celano, Wake Forest University, Chromatic Symmetric Functions and RSK for (3 + 1)-free Posets
Algebra and Combinatorics Seminar: Kyle Celano, Wake Forest University, Chromatic Symmetric Functions and RSK for (3 + 1)-free Posets
In 1995, Stanley introduced the chromatic symmetric function of a graph, a symmetric function analog of the classical chromatic polynomial of a graph. The Stanley-Stembridge e-positivity conjecture is a long-standing conjecture that states that the chromatic symmetric function of a certain class of graphs, called incomparability graphs of (3+1)-free posets, has nonnegative coefficients when expanded…
Nonlinear Analysis Seminar and Differential Equation Seminar: Leon Bungert, University of Würzburg, Adversarial robustness in machine learning: from worst-case to probabilistic
Nonlinear Analysis Seminar and Differential Equation Seminar: Leon Bungert, University of Würzburg, Adversarial robustness in machine learning: from worst-case to probabilistic
In this talk I will first review recent results which characterize adversarial training (AT) of binary classifiers as nonlocal perimeter regularization. Then I will speak about a probabilistic generalization of AT which also admits such a geometric interpretation, albeit with a different nonlocal perimeter. Using suitable relaxations one can prove the existence of solutions for…
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Teaching and Learning Seminar: Maria Meehan, University College Dublin, Video recordings to complement, or substitute for, the first-year mathematics lecture: One lecturer’s journey
Teaching and Learning Seminar: Maria Meehan, University College Dublin, Video recordings to complement, or substitute for, the first-year mathematics lecture: One lecturer’s journey
As part of a professional development project aimed at engaging in the Discipline of Noticing as conceptualised by John Mason, some colleagues and I wrote and shared brief-but-vivid accounts of our practice. Evident in these accounts is the catalyst for the subsequent change in my practice of introducing short, pre-recorded videos to complement, or substitute…
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Computational and Applied Mathematics Seminar: Gregory Ongie, Marquette University, A function space view of infinite-width neural networks
Computational and Applied Mathematics Seminar: Gregory Ongie, Marquette University, A function space view of infinite-width neural networks
It is well-known that nearly any function can be approximated arbitrarily-well by a neural network with non-linear activations. However, one cannot guarantee that the weights in the neural network remain bounded in norm as the approximation error goes to zero, which is an important consideration when practically training neural networks. This raises the question: What…
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